From 8f2f40c71caa623838f4fb3d5923e1169a316fda Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Sergio=20S=C3=A1nchez=20Ram=C3=ADrez?=
 <sergio.sanchez.ramirez+git@bsc.es>
Date: Wed, 10 Jan 2024 21:11:17 +0100
Subject: [PATCH 01/49] Implement `contraction_sequence` with EinExprs
 optimizers

---
 Project.toml                 |  2 ++
 src/contraction_sequences.jl | 14 ++++++++++++++
 2 files changed, 16 insertions(+)

diff --git a/Project.toml b/Project.toml
index 4b9eee8c..d68c415d 100644
--- a/Project.toml
+++ b/Project.toml
@@ -12,6 +12,7 @@ DataStructures = "864edb3b-99cc-5e75-8d2d-829cb0a9cfe8"
 Dictionaries = "85a47980-9c8c-11e8-2b9f-f7ca1fa99fb4"
 Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f"
 DocStringExtensions = "ffbed154-4ef7-542d-bbb7-c09d3a79fcae"
+EinExprs = "b1794770-133b-4de1-afb4-526377e9f4c5"
 Graphs = "86223c79-3864-5bf0-83f7-82e725a168b6"
 GraphsFlows = "06909019-6f44-4949-96fc-b9d9aaa02889"
 ITensors = "9136182c-28ba-11e9-034c-db9fb085ebd5"
@@ -40,6 +41,7 @@ DataStructures = "0.18"
 Dictionaries = "0.3.15"
 Distributions = "0.25.86"
 DocStringExtensions = "0.8, 0.9"
+EinExprs = "0.5"
 Graphs = "1.8"
 GraphsFlows = "0.1.1"
 ITensors = "0.3.23"
diff --git a/src/contraction_sequences.jl b/src/contraction_sequences.jl
index c32239a5..91d07091 100644
--- a/src/contraction_sequences.jl
+++ b/src/contraction_sequences.jl
@@ -119,3 +119,17 @@ function contraction_sequence(::Algorithm"kahypar_bipartite", tn; kwargs...)
     tn; optimizer=OMEinsumContractionOrders.KaHyParBipartite(; kwargs...)
   )
 end
+
+function contraction_sequence(::Algorithm"einexpr", tn; optimizer=EinExprs.Exhaustive())
+  is = IndsNetwork(tn)
+  size_dict = Dict(
+    Symbol(id(index)) => dim(index) for
+    index in Iterators.map(i -> only(is[i]), vertices(is))
+  )
+
+  tensors = map(vertex_data(ψ)) do tensor
+    EinExpr(collect(map(Symbol ∘ id, inds(tensor))))
+  end
+
+  return tn = einexpr(optimizer, EinExpr(tensors, size_dict))
+end

From 21220ebdc3ad543e7cb10bda00745c7bd92f1207 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Sergio=20S=C3=A1nchez=20Ram=C3=ADrez?=
 <sergio.sanchez.ramirez+git@bsc.es>
Date: Wed, 10 Jan 2024 23:31:14 +0100
Subject: [PATCH 02/49] Refactor code

---
 src/contraction_sequences.jl | 15 +++++++++------
 1 file changed, 9 insertions(+), 6 deletions(-)

diff --git a/src/contraction_sequences.jl b/src/contraction_sequences.jl
index 91d07091..195a8ef9 100644
--- a/src/contraction_sequences.jl
+++ b/src/contraction_sequences.jl
@@ -122,14 +122,17 @@ end
 
 function contraction_sequence(::Algorithm"einexpr", tn; optimizer=EinExprs.Exhaustive())
   is = IndsNetwork(tn)
-  size_dict = Dict(
-    Symbol(id(index)) => dim(index) for
-    index in Iterators.map(i -> only(is[i]), vertices(is))
-  )
 
   tensors = map(vertex_data(ψ)) do tensor
-    EinExpr(collect(map(Symbol ∘ id, inds(tensor))))
+    _inds = collect(map(Symbol ∘ id, inds(tensor)))
+    _size = Dict(_inds .=> size(tensor))
+    EinExpr(_inds, _size)
   end
 
-  return tn = einexpr(optimizer, EinExpr(tensors, size_dict))
+  # TODO (mofeing) list open indices
+  expr = sum(tensors; skip=...)
+  path = einexpr(optimizer, expr)
+
+  # TODO (mofeing) convert EinExpr to contraction sequence
+  return nothing
 end

From 6692b1309b2a9c4c85fd018150eb68489d5bbcdc Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Sergio=20S=C3=A1nchez=20Ram=C3=ADrez?=
 <sergio.sanchez.ramirez+git@bsc.es>
Date: Thu, 11 Jan 2024 17:24:17 +0100
Subject: [PATCH 03/49] Skip contraction of `externalinds`

---
 src/contraction_sequences.jl | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/src/contraction_sequences.jl b/src/contraction_sequences.jl
index 195a8ef9..24a92f07 100644
--- a/src/contraction_sequences.jl
+++ b/src/contraction_sequences.jl
@@ -129,8 +129,8 @@ function contraction_sequence(::Algorithm"einexpr", tn; optimizer=EinExprs.Exhau
     EinExpr(_inds, _size)
   end
 
-  # TODO (mofeing) list open indices
-  expr = sum(tensors; skip=...)
+  _openinds = collect(map(Symbol ∘ id, externalinds(tn)))
+  expr = sum(tensors; skip=_openinds)
   path = einexpr(optimizer, expr)
 
   # TODO (mofeing) convert EinExpr to contraction sequence

From cd3ea8f2ba26f62f8c27160470e1037a783d9eb7 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Sergio=20S=C3=A1nchez=20Ram=C3=ADrez?=
 <sergio.sanchez.ramirez+git@bsc.es>
Date: Thu, 11 Jan 2024 17:24:43 +0100
Subject: [PATCH 04/49] Fix typo

---
 src/contraction_sequences.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/contraction_sequences.jl b/src/contraction_sequences.jl
index 24a92f07..e683aed4 100644
--- a/src/contraction_sequences.jl
+++ b/src/contraction_sequences.jl
@@ -123,7 +123,7 @@ end
 function contraction_sequence(::Algorithm"einexpr", tn; optimizer=EinExprs.Exhaustive())
   is = IndsNetwork(tn)
 
-  tensors = map(vertex_data(ψ)) do tensor
+  tensors = map(vertex_data(tn)) do tensor
     _inds = collect(map(Symbol ∘ id, inds(tensor)))
     _size = Dict(_inds .=> size(tensor))
     EinExpr(_inds, _size)

From d4b0ea18be62b0512b8360d64665350180a51afc Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Sergio=20S=C3=A1nchez=20Ram=C3=ADrez?=
 <sergio.sanchez.ramirez+git@bsc.es>
Date: Thu, 11 Jan 2024 17:45:57 +0100
Subject: [PATCH 05/49] Import `EinExprs` symbols

---
 src/contraction_sequences.jl | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/src/contraction_sequences.jl b/src/contraction_sequences.jl
index e683aed4..b72da7e5 100644
--- a/src/contraction_sequences.jl
+++ b/src/contraction_sequences.jl
@@ -1,3 +1,5 @@
+using EinExprs: EinExprs, EinExpr, einexpr
+
 function contraction_sequence(tn::Vector{ITensor}; alg="optimal", kwargs...)
   return contraction_sequence(Algorithm(alg), tn; kwargs...)
 end

From 11f2df0a8bc17b4545a0f61fc38d944140ed4faa Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Sergio=20S=C3=A1nchez=20Ram=C3=ADrez?=
 <sergio.sanchez.ramirez+git@bsc.es>
Date: Thu, 11 Jan 2024 17:46:22 +0100
Subject: [PATCH 06/49] Fix resulting type of `map` on tensors

---
 src/contraction_sequences.jl | 4 +---
 1 file changed, 1 insertion(+), 3 deletions(-)

diff --git a/src/contraction_sequences.jl b/src/contraction_sequences.jl
index b72da7e5..a0580392 100644
--- a/src/contraction_sequences.jl
+++ b/src/contraction_sequences.jl
@@ -123,9 +123,7 @@ function contraction_sequence(::Algorithm"kahypar_bipartite", tn; kwargs...)
 end
 
 function contraction_sequence(::Algorithm"einexpr", tn; optimizer=EinExprs.Exhaustive())
-  is = IndsNetwork(tn)
-
-  tensors = map(vertex_data(tn)) do tensor
+  tensors = map(tokenized(vertex_data(tn))) do tensor
     _inds = collect(map(Symbol ∘ id, inds(tensor)))
     _size = Dict(_inds .=> size(tensor))
     EinExpr(_inds, _size)

From c412bb8917bf2600af84a4f8a2666b9bcc037d93 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Sergio=20S=C3=A1nchez=20Ram=C3=ADrez?=
 <sergio.sanchez.ramirez+git@bsc.es>
Date: Thu, 11 Jan 2024 18:25:48 +0100
Subject: [PATCH 07/49] Map `EinExpr` to expected contraction sequence format
 by `ITensorNetworks`

---
 src/contraction_sequences.jl | 21 ++++++++++++++-------
 1 file changed, 14 insertions(+), 7 deletions(-)

diff --git a/src/contraction_sequences.jl b/src/contraction_sequences.jl
index a0580392..892af423 100644
--- a/src/contraction_sequences.jl
+++ b/src/contraction_sequences.jl
@@ -123,16 +123,23 @@ function contraction_sequence(::Algorithm"kahypar_bipartite", tn; kwargs...)
 end
 
 function contraction_sequence(::Algorithm"einexpr", tn; optimizer=EinExprs.Exhaustive())
-  tensors = map(tokenized(vertex_data(tn))) do tensor
-    _inds = collect(map(Symbol ∘ id, inds(tensor)))
-    _size = Dict(_inds .=> size(tensor))
-    EinExpr(_inds, _size)
-  end
+  tensor_map = IdDict(
+    map(pairs(vertex_data(tn))) do (key, tensor)
+      _inds = collect(map(Symbol ∘ id, inds(tensor)))
+      _size = Dict(_inds .=> size(tensor))
+      EinExpr(_inds, _size) => key
+    end,
+  )
+  tensors = collect(keys(tensor_map))
 
   _openinds = collect(map(Symbol ∘ id, externalinds(tn)))
   expr = sum(tensors; skip=_openinds)
   path = einexpr(optimizer, expr)
 
-  # TODO (mofeing) convert EinExpr to contraction sequence
-  return nothing
+  function _convert_to_contraction_sequence(subpath)
+    length(subpath.args) == 0 && return tensor_map[subpath]
+    return map(_convert_to_contraction_sequence, subpath.args)
+  end
+
+  return _convert_to_contraction_sequence(path)
 end

From 8e83fb2f11c6e2602e61918af989f0fbba73fc17 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Sergio=20S=C3=A1nchez=20Ram=C3=ADrez?=
 <sergio.sanchez.ramirez+git@bsc.es>
Date: Thu, 11 Jan 2024 19:01:51 +0100
Subject: [PATCH 08/49] Move code to package extension

---
 Project.toml                      |  7 ++++++-
 ext/ITensorNetworksEinExprsExt.jl | 30 ++++++++++++++++++++++++++++++
 src/contraction_sequences.jl      | 24 ------------------------
 3 files changed, 36 insertions(+), 25 deletions(-)
 create mode 100644 ext/ITensorNetworksEinExprsExt.jl

diff --git a/Project.toml b/Project.toml
index d68c415d..2c1c6673 100644
--- a/Project.toml
+++ b/Project.toml
@@ -12,7 +12,6 @@ DataStructures = "864edb3b-99cc-5e75-8d2d-829cb0a9cfe8"
 Dictionaries = "85a47980-9c8c-11e8-2b9f-f7ca1fa99fb4"
 Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f"
 DocStringExtensions = "ffbed154-4ef7-542d-bbb7-c09d3a79fcae"
-EinExprs = "b1794770-133b-4de1-afb4-526377e9f4c5"
 Graphs = "86223c79-3864-5bf0-83f7-82e725a168b6"
 GraphsFlows = "06909019-6f44-4949-96fc-b9d9aaa02889"
 ITensors = "9136182c-28ba-11e9-034c-db9fb085ebd5"
@@ -32,6 +31,12 @@ Suppressor = "fd094767-a336-5f1f-9728-57cf17d0bbfb"
 TimerOutputs = "a759f4b9-e2f1-59dc-863e-4aeb61b1ea8f"
 TupleTools = "9d95972d-f1c8-5527-a6e0-b4b365fa01f6"
 
+[weakdeps]
+EinExprs = "b1794770-133b-4de1-afb4-526377e9f4c5"
+
+[extensions]
+ITensorNetworksEinExprsExt = "EinExprs"
+
 [compat]
 AbstractTrees = "0.4.4"
 Combinatorics = "1"
diff --git a/ext/ITensorNetworksEinExprsExt.jl b/ext/ITensorNetworksEinExprsExt.jl
new file mode 100644
index 00000000..8b97648f
--- /dev/null
+++ b/ext/ITensorNetworksEinExprsExt.jl
@@ -0,0 +1,30 @@
+module ITensorNetworksEinExprsExt
+
+using ITensorNetworks
+using EinExprs: EinExprs, EinExpr, einexpr
+
+function ITensorNetworks.contraction_sequence(
+  ::ITensorNetworks.Algorithm"einexpr", tn; optimizer=EinExprs.Exhaustive()
+)
+  tensor_map = IdDict(
+    map(pairs(vertex_data(tn))) do (key, tensor)
+      _inds = collect(map(Symbol ∘ id, inds(tensor)))
+      _size = Dict(_inds .=> size(tensor))
+      EinExpr(_inds, _size) => key
+    end,
+  )
+  tensors = collect(keys(tensor_map))
+
+  _openinds = collect(map(Symbol ∘ id, externalinds(tn)))
+  expr = sum(tensors; skip=_openinds)
+  path = einexpr(optimizer, expr)
+
+  function _convert_to_contraction_sequence(subpath)
+    length(subpath.args) == 0 && return tensor_map[subpath]
+    return map(_convert_to_contraction_sequence, subpath.args)
+  end
+
+  return _convert_to_contraction_sequence(path)
+end
+
+end
diff --git a/src/contraction_sequences.jl b/src/contraction_sequences.jl
index 892af423..c32239a5 100644
--- a/src/contraction_sequences.jl
+++ b/src/contraction_sequences.jl
@@ -1,5 +1,3 @@
-using EinExprs: EinExprs, EinExpr, einexpr
-
 function contraction_sequence(tn::Vector{ITensor}; alg="optimal", kwargs...)
   return contraction_sequence(Algorithm(alg), tn; kwargs...)
 end
@@ -121,25 +119,3 @@ function contraction_sequence(::Algorithm"kahypar_bipartite", tn; kwargs...)
     tn; optimizer=OMEinsumContractionOrders.KaHyParBipartite(; kwargs...)
   )
 end
-
-function contraction_sequence(::Algorithm"einexpr", tn; optimizer=EinExprs.Exhaustive())
-  tensor_map = IdDict(
-    map(pairs(vertex_data(tn))) do (key, tensor)
-      _inds = collect(map(Symbol ∘ id, inds(tensor)))
-      _size = Dict(_inds .=> size(tensor))
-      EinExpr(_inds, _size) => key
-    end,
-  )
-  tensors = collect(keys(tensor_map))
-
-  _openinds = collect(map(Symbol ∘ id, externalinds(tn)))
-  expr = sum(tensors; skip=_openinds)
-  path = einexpr(optimizer, expr)
-
-  function _convert_to_contraction_sequence(subpath)
-    length(subpath.args) == 0 && return tensor_map[subpath]
-    return map(_convert_to_contraction_sequence, subpath.args)
-  end
-
-  return _convert_to_contraction_sequence(path)
-end

From 16a0fcdb2f3311383f70307d2d1d2d5b5191367a Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Sergio=20S=C3=A1nchez=20Ram=C3=ADrez?=
 <sergio.sanchez.ramirez+git@bsc.es>
Date: Fri, 26 Jan 2024 15:07:53 +0100
Subject: [PATCH 09/49] Update EinExprs to v0.6

---
 Project.toml                      | 2 +-
 ext/ITensorNetworksEinExprsExt.jl | 4 ++--
 2 files changed, 3 insertions(+), 3 deletions(-)

diff --git a/Project.toml b/Project.toml
index 2c1c6673..0ee65a49 100644
--- a/Project.toml
+++ b/Project.toml
@@ -46,7 +46,7 @@ DataStructures = "0.18"
 Dictionaries = "0.3.15"
 Distributions = "0.25.86"
 DocStringExtensions = "0.8, 0.9"
-EinExprs = "0.5"
+EinExprs = "0.6"
 Graphs = "1.8"
 GraphsFlows = "0.1.1"
 ITensors = "0.3.23"
diff --git a/ext/ITensorNetworksEinExprsExt.jl b/ext/ITensorNetworksEinExprsExt.jl
index 8b97648f..c1d44f27 100644
--- a/ext/ITensorNetworksEinExprsExt.jl
+++ b/ext/ITensorNetworksEinExprsExt.jl
@@ -8,14 +8,14 @@ function ITensorNetworks.contraction_sequence(
 )
   tensor_map = IdDict(
     map(pairs(vertex_data(tn))) do (key, tensor)
-      _inds = collect(map(Symbol ∘ id, inds(tensor)))
+      _inds = collect(ITensorNetworks.inds(tensor))
       _size = Dict(_inds .=> size(tensor))
       EinExpr(_inds, _size) => key
     end,
   )
   tensors = collect(keys(tensor_map))
 
-  _openinds = collect(map(Symbol ∘ id, externalinds(tn)))
+  _openinds = collect(ITensorNetworks.externalinds(tn))
   expr = sum(tensors; skip=_openinds)
   path = einexpr(optimizer, expr)
 

From 92fcf8183f0028b9e9fbde66d270029a6ca3a2b7 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Sergio=20S=C3=A1nchez=20Ram=C3=ADrez?=
 <sergio.sanchez.ramirez+git@bsc.es>
Date: Mon, 29 Jan 2024 10:19:02 +0100
Subject: [PATCH 10/49] Fixes

---
 ext/ITensorNetworksEinExprsExt.jl | 35 ++++++++++++++++++-------------
 1 file changed, 21 insertions(+), 14 deletions(-)

diff --git a/ext/ITensorNetworksEinExprsExt.jl b/ext/ITensorNetworksEinExprsExt.jl
index c1d44f27..5d4ef6d3 100644
--- a/ext/ITensorNetworksEinExprsExt.jl
+++ b/ext/ITensorNetworksEinExprsExt.jl
@@ -1,27 +1,34 @@
 module ITensorNetworksEinExprsExt
 
 using ITensorNetworks
-using EinExprs: EinExprs, EinExpr, einexpr
+using ITensorNetworks: Index
+using EinExprs: EinExprs, EinExpr, einexpr, SizedEinExpr
 
 function ITensorNetworks.contraction_sequence(
-  ::ITensorNetworks.Algorithm"einexpr", tn; optimizer=EinExprs.Exhaustive()
-)
-  tensor_map = IdDict(
-    map(pairs(vertex_data(tn))) do (key, tensor)
-      _inds = collect(ITensorNetworks.inds(tensor))
-      _size = Dict(_inds .=> size(tensor))
-      EinExpr(_inds, _size) => key
-    end,
-  )
-  tensors = collect(keys(tensor_map))
+  ::ITensorNetworks.Algorithm"einexpr",
+  tn::ITensorNetwork{T};
+  optimizer=EinExprs.Exhaustive(),
+) where {T}
+  IndexType = Any
+
+  tensors = EinExpr{IndexType}[]
+  tensor_map = Dict{Set{IndexType},T}()
+  sizedict = Dict{IndexType,Int}()
+
+  for (key, tensor) in pairs(vertex_data(tn))
+    _inds = collect(ITensorNetworks.inds(tensor))
+    push!(tensors, EinExpr{IndexType}(; head=_inds))
+    tensor_map[Set(_inds)] = key
+    merge!(sizedict, Dict(_inds .=> size(tensor)))
+  end
 
   _openinds = collect(ITensorNetworks.externalinds(tn))
-  expr = sum(tensors; skip=_openinds)
+  expr = SizedEinExpr(sum(tensors; skip=_openinds), sizedict)
   path = einexpr(optimizer, expr)
 
   function _convert_to_contraction_sequence(subpath)
-    length(subpath.args) == 0 && return tensor_map[subpath]
-    return map(_convert_to_contraction_sequence, subpath.args)
+    EinExprs.nargs(subpath) == 0 && return tensor_map[Set(subpath.head)]
+    return map(_convert_to_contraction_sequence, EinExprs.args(subpath))
   end
 
   return _convert_to_contraction_sequence(path)

From b0fa2ab8dbd912241f19b8a1f3fb9f621f8b3a85 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Sergio=20S=C3=A1nchez=20Ram=C3=ADrez?=
 <sergio.sanchez.ramirez+git@bsc.es>
Date: Mon, 29 Jan 2024 17:47:44 +0100
Subject: [PATCH 11/49] Refactor `externalinds` reference

---
 ext/ITensorNetworksEinExprsExt.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/ext/ITensorNetworksEinExprsExt.jl b/ext/ITensorNetworksEinExprsExt.jl
index 5d4ef6d3..256dc736 100644
--- a/ext/ITensorNetworksEinExprsExt.jl
+++ b/ext/ITensorNetworksEinExprsExt.jl
@@ -22,7 +22,7 @@ function ITensorNetworks.contraction_sequence(
     merge!(sizedict, Dict(_inds .=> size(tensor)))
   end
 
-  _openinds = collect(ITensorNetworks.externalinds(tn))
+  _openinds = collect(externalinds(tn))
   expr = SizedEinExpr(sum(tensors; skip=_openinds), sizedict)
   path = einexpr(optimizer, expr)
 

From 21c5728dc8927d57f541fc2eb00ed0cff2085f14 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Sergio=20S=C3=A1nchez=20Ram=C3=ADrez?=
 <sergio.sanchez.ramirez+git@bsc.es>
Date: Tue, 6 Feb 2024 11:00:37 +0100
Subject: [PATCH 12/49] Refactor code

---
 ext/ITensorNetworksEinExprsExt.jl | 17 +++++++++++------
 1 file changed, 11 insertions(+), 6 deletions(-)

diff --git a/ext/ITensorNetworksEinExprsExt.jl b/ext/ITensorNetworksEinExprsExt.jl
index 256dc736..2fc78af6 100644
--- a/ext/ITensorNetworksEinExprsExt.jl
+++ b/ext/ITensorNetworksEinExprsExt.jl
@@ -4,11 +4,7 @@ using ITensorNetworks
 using ITensorNetworks: Index
 using EinExprs: EinExprs, EinExpr, einexpr, SizedEinExpr
 
-function ITensorNetworks.contraction_sequence(
-  ::ITensorNetworks.Algorithm"einexpr",
-  tn::ITensorNetwork{T};
-  optimizer=EinExprs.Exhaustive(),
-) where {T}
+function EinExprs.einexpr(tn::ITensorNetwork{T}; optimizer::EinExprs.Optimizer) where {T}
   IndexType = Any
 
   tensors = EinExpr{IndexType}[]
@@ -24,7 +20,16 @@ function ITensorNetworks.contraction_sequence(
 
   _openinds = collect(externalinds(tn))
   expr = SizedEinExpr(sum(tensors; skip=_openinds), sizedict)
-  path = einexpr(optimizer, expr)
+
+  return einexpr(optimizer, expr)
+end
+
+function ITensorNetworks.contraction_sequence(
+  ::ITensorNetworks.Algorithm"einexpr",
+  tn::ITensorNetwork{T};
+  optimizer=EinExprs.Exhaustive(),
+) where {T}
+  path = einexpr(tn; optimizer)
 
   function _convert_to_contraction_sequence(subpath)
     EinExprs.nargs(subpath) == 0 && return tensor_map[Set(subpath.head)]

From 7bf59be972e0fdaf5e07ebcdfed10e73013bf022 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Sergio=20S=C3=A1nchez=20Ram=C3=ADrez?=
 <sergio.sanchez.ramirez+git@bsc.es>
Date: Tue, 6 Feb 2024 14:47:50 +0100
Subject: [PATCH 13/49] Test `EinExprs` code

---
 test/Project.toml                 |  1 +
 test/test_contraction_sequence.jl | 15 ++++++++++++++-
 2 files changed, 15 insertions(+), 1 deletion(-)

diff --git a/test/Project.toml b/test/Project.toml
index f9f1d11f..05386c5c 100644
--- a/test/Project.toml
+++ b/test/Project.toml
@@ -4,6 +4,7 @@ Compat = "34da2185-b29b-5c13-b0c7-acf172513d20"
 Dictionaries = "85a47980-9c8c-11e8-2b9f-f7ca1fa99fb4"
 DifferentialEquations = "0c46a032-eb83-5123-abaf-570d42b7fbaa"
 Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f"
+EinExprs = "b1794770-133b-4de1-afb4-526377e9f4c5"
 Glob = "c27321d9-0574-5035-807b-f59d2c89b15c"
 Graphs = "86223c79-3864-5bf0-83f7-82e725a168b6"
 GraphsFlows = "06909019-6f44-4949-96fc-b9d9aaa02889"
diff --git a/test/test_contraction_sequence.jl b/test/test_contraction_sequence.jl
index fd732f3f..2184db22 100644
--- a/test/test_contraction_sequence.jl
+++ b/test/test_contraction_sequence.jl
@@ -3,6 +3,7 @@ using ITensorNetworks
 using OMEinsumContractionOrders
 using Random
 using Test
+using EinExprs: Exhaustive, Greedy, HyPar
 
 Random.seed!(1234)
 
@@ -23,7 +24,19 @@ ITensors.disable_warn_order()
   res_tree_sa = contract(tn; sequence=seq_tree_sa)[]
   seq_sa_bipartite = contraction_sequence(tn; alg="sa_bipartite")
   res_sa_bipartite = contract(tn; sequence=seq_sa_bipartite)[]
-  @test res_optimal ≈ res_greedy ≈ res_tree_sa ≈ res_sa_bipartite
+  seq_einexprs_exhaustive = contraction_sequence(tn; alg="einexpr", optimizer=Exhaustive())
+  res_einexprs_exhaustive = contract(tn; sequence=seq_einexprs_exhaustive)[]
+  seq_einexprs_greedy = contraction_sequence(tn; alg="einexpr", optimizer=Greedy())
+  res_einexprs_greedy = contract(tn; sequence=seq_einexprs_exhaustive)[]
+  seq_einexprs_kahypar = contraction_sequence(tn; alg="einexpr", optimizer=HyPar())
+  res_einexprs_kahypar = contract(tn; sequence=seq_einexprs_kahypar)[]
+  @test res_optimal ≈
+    res_greedy ≈
+    res_tree_sa ≈
+    res_sa_bipartite ≈
+    res_einexprs_exhaustive ≈
+    res_einexprs_greedy ≈
+    res_einexprs_kahypar
 
   if !Sys.iswindows()
     # KaHyPar doesn't work on Windows

From e405493697845114688acf6994e50fc89b1f486f Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Sergio=20S=C3=A1nchez=20Ram=C3=ADrez?=
 <sergio.sanchez.ramirez+git@bsc.es>
Date: Tue, 6 Feb 2024 14:49:06 +0100
Subject: [PATCH 14/49] Fix `contraction_sequence` interface

---
 ext/ITensorNetworksEinExprsExt.jl | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/ext/ITensorNetworksEinExprsExt.jl b/ext/ITensorNetworksEinExprsExt.jl
index 2fc78af6..ca9bcfe7 100644
--- a/ext/ITensorNetworksEinExprsExt.jl
+++ b/ext/ITensorNetworksEinExprsExt.jl
@@ -1,5 +1,6 @@
 module ITensorNetworksEinExprsExt
 
+using ITensors
 using ITensorNetworks
 using ITensorNetworks: Index
 using EinExprs: EinExprs, EinExpr, einexpr, SizedEinExpr
@@ -25,10 +26,9 @@ function EinExprs.einexpr(tn::ITensorNetwork{T}; optimizer::EinExprs.Optimizer)
 end
 
 function ITensorNetworks.contraction_sequence(
-  ::ITensorNetworks.Algorithm"einexpr",
-  tn::ITensorNetwork{T};
-  optimizer=EinExprs.Exhaustive(),
-) where {T}
+  ::ITensorNetworks.Algorithm"einexpr", tn::Vector{ITensor}; optimizer=EinExprs.Exhaustive()
+)
+  tn = ITensorNetwork(tn)
   path = einexpr(tn; optimizer)
 
   function _convert_to_contraction_sequence(subpath)

From 5b2fe0d0ca810c10adda63bd74fdb49a1ac65974 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Sergio=20S=C3=A1nchez=20Ram=C3=ADrez?=
 <sergio.sanchez.ramirez+git@bsc.es>
Date: Tue, 6 Feb 2024 14:53:35 +0100
Subject: [PATCH 15/49] Duplicate code to preserve `tensor_map`

---
 ext/ITensorNetworksEinExprsExt.jl | 18 +++++++++++++++++-
 1 file changed, 17 insertions(+), 1 deletion(-)

diff --git a/ext/ITensorNetworksEinExprsExt.jl b/ext/ITensorNetworksEinExprsExt.jl
index ca9bcfe7..788b04a6 100644
--- a/ext/ITensorNetworksEinExprsExt.jl
+++ b/ext/ITensorNetworksEinExprsExt.jl
@@ -29,7 +29,23 @@ function ITensorNetworks.contraction_sequence(
   ::ITensorNetworks.Algorithm"einexpr", tn::Vector{ITensor}; optimizer=EinExprs.Exhaustive()
 )
   tn = ITensorNetwork(tn)
-  path = einexpr(tn; optimizer)
+  IndexType = Any
+
+  tensors = EinExpr{IndexType}[]
+  tensor_map = Dict{Set{IndexType},T}()
+  sizedict = Dict{IndexType,Int}()
+
+  for (key, tensor) in pairs(vertex_data(tn))
+    _inds = collect(ITensorNetworks.inds(tensor))
+    push!(tensors, EinExpr{IndexType}(; head=_inds))
+    tensor_map[Set(_inds)] = key
+    merge!(sizedict, Dict(_inds .=> size(tensor)))
+  end
+
+  _openinds = collect(externalinds(tn))
+  expr = SizedEinExpr(sum(tensors; skip=_openinds), sizedict)
+
+  path = einexpr(optimizer, expr)
 
   function _convert_to_contraction_sequence(subpath)
     EinExprs.nargs(subpath) == 0 && return tensor_map[Set(subpath.head)]

From ad6d896c112c5b989e33e687a3ed0d441b42c4ea Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Sergio=20S=C3=A1nchez=20Ram=C3=ADrez?=
 <sergio.sanchez.ramirez+git@bsc.es>
Date: Tue, 6 Feb 2024 15:04:19 +0100
Subject: [PATCH 16/49] Lasf fixes

---
 ext/ITensorNetworksEinExprsExt.jl | 11 +++++++++--
 1 file changed, 9 insertions(+), 2 deletions(-)

diff --git a/ext/ITensorNetworksEinExprsExt.jl b/ext/ITensorNetworksEinExprsExt.jl
index 788b04a6..2c8b180e 100644
--- a/ext/ITensorNetworksEinExprsExt.jl
+++ b/ext/ITensorNetworksEinExprsExt.jl
@@ -26,9 +26,16 @@ function EinExprs.einexpr(tn::ITensorNetwork{T}; optimizer::EinExprs.Optimizer)
 end
 
 function ITensorNetworks.contraction_sequence(
-  ::ITensorNetworks.Algorithm"einexpr", tn::Vector{ITensor}; optimizer=EinExprs.Exhaustive()
+  alg::ITensorNetworks.Algorithm"einexpr", tn::Vector{ITensor}; kwargs...
 )
-  tn = ITensorNetwork(tn)
+  return contraction_sequence(alg, ITensorNetwork(tn); kwargs...)
+end
+
+function ITensorNetworks.contraction_sequence(
+  ::ITensorNetworks.Algorithm"einexpr",
+  tn::ITensorNetwork{T};
+  optimizer=EinExprs.Exhaustive(),
+) where {T}
   IndexType = Any
 
   tensors = EinExpr{IndexType}[]

From ead70adc97d498cfdbc798d588532ca448e327b9 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Sergio=20S=C3=A1nchez=20Ram=C3=ADrez?=
 <sergio.sanchez.ramirez+git@bsc.es>
Date: Tue, 6 Feb 2024 15:42:38 +0100
Subject: [PATCH 17/49] Restructure package extension

---
 .../src}/ITensorNetworksEinExprsExt.jl                            | 0
 1 file changed, 0 insertions(+), 0 deletions(-)
 rename ext/{ => ITensorNetworksEinExprsExt/src}/ITensorNetworksEinExprsExt.jl (100%)

diff --git a/ext/ITensorNetworksEinExprsExt.jl b/ext/ITensorNetworksEinExprsExt/src/ITensorNetworksEinExprsExt.jl
similarity index 100%
rename from ext/ITensorNetworksEinExprsExt.jl
rename to ext/ITensorNetworksEinExprsExt/src/ITensorNetworksEinExprsExt.jl

From e9acbf462b8911d7fd89eb136ee240922afcfbb4 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Sergio=20S=C3=A1nchez=20Ram=C3=ADrez?=
 <sergio.sanchez.ramirez+git@bsc.es>
Date: Tue, 6 Feb 2024 15:51:57 +0100
Subject: [PATCH 18/49] Remove redundant package specification

---
 .../src/ITensorNetworksEinExprsExt.jl                         | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/ext/ITensorNetworksEinExprsExt/src/ITensorNetworksEinExprsExt.jl b/ext/ITensorNetworksEinExprsExt/src/ITensorNetworksEinExprsExt.jl
index 2c8b180e..7f59bbbf 100644
--- a/ext/ITensorNetworksEinExprsExt/src/ITensorNetworksEinExprsExt.jl
+++ b/ext/ITensorNetworksEinExprsExt/src/ITensorNetworksEinExprsExt.jl
@@ -13,7 +13,7 @@ function EinExprs.einexpr(tn::ITensorNetwork{T}; optimizer::EinExprs.Optimizer)
   sizedict = Dict{IndexType,Int}()
 
   for (key, tensor) in pairs(vertex_data(tn))
-    _inds = collect(ITensorNetworks.inds(tensor))
+    _inds = collect(inds(tensor))
     push!(tensors, EinExpr{IndexType}(; head=_inds))
     tensor_map[Set(_inds)] = key
     merge!(sizedict, Dict(_inds .=> size(tensor)))
@@ -43,7 +43,7 @@ function ITensorNetworks.contraction_sequence(
   sizedict = Dict{IndexType,Int}()
 
   for (key, tensor) in pairs(vertex_data(tn))
-    _inds = collect(ITensorNetworks.inds(tensor))
+    _inds = collect(inds(tensor))
     push!(tensors, EinExpr{IndexType}(; head=_inds))
     tensor_map[Set(_inds)] = key
     merge!(sizedict, Dict(_inds .=> size(tensor)))

From e3ca80f26c19245d8779ba4bce12745678dc8ec5 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Sergio=20S=C3=A1nchez=20Ram=C3=ADrez?=
 <sergio.sanchez.ramirez+git@bsc.es>
Date: Tue, 6 Feb 2024 15:53:25 +0100
Subject: [PATCH 19/49] Apply suggestion by @mtfishman

---
 .../src/ITensorNetworksEinExprsExt.jl                          | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/ext/ITensorNetworksEinExprsExt/src/ITensorNetworksEinExprsExt.jl b/ext/ITensorNetworksEinExprsExt/src/ITensorNetworksEinExprsExt.jl
index 7f59bbbf..99e8a6a1 100644
--- a/ext/ITensorNetworksEinExprsExt/src/ITensorNetworksEinExprsExt.jl
+++ b/ext/ITensorNetworksEinExprsExt/src/ITensorNetworksEinExprsExt.jl
@@ -5,8 +5,9 @@ using ITensorNetworks
 using ITensorNetworks: Index
 using EinExprs: EinExprs, EinExpr, einexpr, SizedEinExpr
 
-function EinExprs.einexpr(tn::ITensorNetwork{T}; optimizer::EinExprs.Optimizer) where {T}
+function EinExprs.einexpr(tn::ITensorNetwork; optimizer::EinExprs.Optimizer)
   IndexType = Any
+  T = vertextype(tn)
 
   tensors = EinExpr{IndexType}[]
   tensor_map = Dict{Set{IndexType},T}()

From 6d6eea224f3c9cf415da92c1574b2e258df6334e Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Sergio=20S=C3=A1nchez=20Ram=C3=ADrez?=
 <sergio.sanchez.ramirez+git@bsc.es>
Date: Tue, 6 Feb 2024 15:57:33 +0100
Subject: [PATCH 20/49] Apply suggestion by @mtfishman

---
 .../src/ITensorNetworksEinExprsExt.jl                          | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/ext/ITensorNetworksEinExprsExt/src/ITensorNetworksEinExprsExt.jl b/ext/ITensorNetworksEinExprsExt/src/ITensorNetworksEinExprsExt.jl
index 99e8a6a1..15fd8dbc 100644
--- a/ext/ITensorNetworksEinExprsExt/src/ITensorNetworksEinExprsExt.jl
+++ b/ext/ITensorNetworksEinExprsExt/src/ITensorNetworksEinExprsExt.jl
@@ -36,8 +36,9 @@ function ITensorNetworks.contraction_sequence(
   ::ITensorNetworks.Algorithm"einexpr",
   tn::ITensorNetwork{T};
   optimizer=EinExprs.Exhaustive(),
-) where {T}
+)
   IndexType = Any
+  T = vertextype(tn)
 
   tensors = EinExpr{IndexType}[]
   tensor_map = Dict{Set{IndexType},T}()

From 55169513d35098658395bc83c1bd5c7e050ab20b Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Sergio=20S=C3=A1nchez=20Ram=C3=ADrez?=
 <sergio.sanchez.ramirez+git@bsc.es>
Date: Tue, 6 Feb 2024 16:02:10 +0100
Subject: [PATCH 21/49] Apply suggestion by @mtfishman

---
 .../src/ITensorNetworksEinExprsExt.jl          | 18 +++++++++++-------
 1 file changed, 11 insertions(+), 7 deletions(-)

diff --git a/ext/ITensorNetworksEinExprsExt/src/ITensorNetworksEinExprsExt.jl b/ext/ITensorNetworksEinExprsExt/src/ITensorNetworksEinExprsExt.jl
index 15fd8dbc..d1e99a24 100644
--- a/ext/ITensorNetworksEinExprsExt/src/ITensorNetworksEinExprsExt.jl
+++ b/ext/ITensorNetworksEinExprsExt/src/ITensorNetworksEinExprsExt.jl
@@ -1,8 +1,14 @@
 module ITensorNetworksEinExprsExt
 
-using ITensors
-using ITensorNetworks
-using ITensorNetworks: Index
+using ITensors: Index, ITensor
+using ITensorNetworks:
+  ITensorNetworks,
+  ITensorNetwork,
+  vertextype,
+  vertex_data,
+  externalinds,
+  contraction_sequence,
+  Algorithm
 using EinExprs: EinExprs, EinExpr, einexpr, SizedEinExpr
 
 function EinExprs.einexpr(tn::ITensorNetwork; optimizer::EinExprs.Optimizer)
@@ -27,15 +33,13 @@ function EinExprs.einexpr(tn::ITensorNetwork; optimizer::EinExprs.Optimizer)
 end
 
 function ITensorNetworks.contraction_sequence(
-  alg::ITensorNetworks.Algorithm"einexpr", tn::Vector{ITensor}; kwargs...
+  alg::Algorithm"einexpr", tn::Vector{ITensor}; kwargs...
 )
   return contraction_sequence(alg, ITensorNetwork(tn); kwargs...)
 end
 
 function ITensorNetworks.contraction_sequence(
-  ::ITensorNetworks.Algorithm"einexpr",
-  tn::ITensorNetwork{T};
-  optimizer=EinExprs.Exhaustive(),
+  ::Algorithm"einexpr", tn::ITensorNetwork{T}; optimizer=EinExprs.Exhaustive()
 )
   IndexType = Any
   T = vertextype(tn)

From 33da278b4773a27a0f4f8a56988fe9b7f63b76d3 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Sergio=20S=C3=A1nchez=20Ram=C3=ADrez?=
 <sergio.sanchez.ramirez+git@bsc.es>
Date: Tue, 6 Feb 2024 16:05:15 +0100
Subject: [PATCH 22/49] More suggestions by @mtfishman

---
 .../src/ITensorNetworksEinExprsExt.jl               | 13 ++++++-------
 1 file changed, 6 insertions(+), 7 deletions(-)

diff --git a/ext/ITensorNetworksEinExprsExt/src/ITensorNetworksEinExprsExt.jl b/ext/ITensorNetworksEinExprsExt/src/ITensorNetworksEinExprsExt.jl
index d1e99a24..d3f641cb 100644
--- a/ext/ITensorNetworksEinExprsExt/src/ITensorNetworksEinExprsExt.jl
+++ b/ext/ITensorNetworksEinExprsExt/src/ITensorNetworksEinExprsExt.jl
@@ -1,22 +1,21 @@
 module ITensorNetworksEinExprsExt
 
-using ITensors: Index, ITensor
+using ITensors: Index, ITensor, Algorithm
 using ITensorNetworks:
   ITensorNetworks,
   ITensorNetwork,
   vertextype,
   vertex_data,
   externalinds,
-  contraction_sequence,
-  Algorithm
+  contraction_sequence
 using EinExprs: EinExprs, EinExpr, einexpr, SizedEinExpr
 
 function EinExprs.einexpr(tn::ITensorNetwork; optimizer::EinExprs.Optimizer)
   IndexType = Any
-  T = vertextype(tn)
+  VertexType = vertextype(tn)
 
   tensors = EinExpr{IndexType}[]
-  tensor_map = Dict{Set{IndexType},T}()
+  tensor_map = Dict{Set{IndexType},VertexType}()
   sizedict = Dict{IndexType,Int}()
 
   for (key, tensor) in pairs(vertex_data(tn))
@@ -42,10 +41,10 @@ function ITensorNetworks.contraction_sequence(
   ::Algorithm"einexpr", tn::ITensorNetwork{T}; optimizer=EinExprs.Exhaustive()
 )
   IndexType = Any
-  T = vertextype(tn)
+  VertexType = vertextype(tn)
 
   tensors = EinExpr{IndexType}[]
-  tensor_map = Dict{Set{IndexType},T}()
+  tensor_map = Dict{Set{IndexType},VertexType}()
   sizedict = Dict{IndexType,Int}()
 
   for (key, tensor) in pairs(vertex_data(tn))

From 053cf87dd18f70fbb78a58bb6fbc410859bafdad Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Sergio=20S=C3=A1nchez=20Ram=C3=ADrez?=
 <sergio.sanchez.ramirez+git@bsc.es>
Date: Tue, 6 Feb 2024 16:14:42 +0100
Subject: [PATCH 23/49] Apply style suggestions by @mtfishman

---
 .../src/ITensorNetworksEinExprsExt.jl         | 30 ++++++++++---------
 1 file changed, 16 insertions(+), 14 deletions(-)

diff --git a/ext/ITensorNetworksEinExprsExt/src/ITensorNetworksEinExprsExt.jl b/ext/ITensorNetworksEinExprsExt/src/ITensorNetworksEinExprsExt.jl
index d3f641cb..b146b482 100644
--- a/ext/ITensorNetworksEinExprsExt/src/ITensorNetworksEinExprsExt.jl
+++ b/ext/ITensorNetworksEinExprsExt/src/ITensorNetworksEinExprsExt.jl
@@ -18,15 +18,16 @@ function EinExprs.einexpr(tn::ITensorNetwork; optimizer::EinExprs.Optimizer)
   tensor_map = Dict{Set{IndexType},VertexType}()
   sizedict = Dict{IndexType,Int}()
 
-  for (key, tensor) in pairs(vertex_data(tn))
-    _inds = collect(inds(tensor))
-    push!(tensors, EinExpr{IndexType}(; head=_inds))
-    tensor_map[Set(_inds)] = key
-    merge!(sizedict, Dict(_inds .=> size(tensor)))
+  for v in vertices(tn)
+    tensor_v = tn[v]
+    inds_v = collect(inds(tensor_v))
+    push!(tensors, EinExpr{IndexType}(; head=inds_v))
+    tensor_map[Set(inds_v)] = key
+    merge!(sizedict, Dict(inds_v .=> size(tensor_v)))
   end
 
-  _openinds = collect(externalinds(tn))
-  expr = SizedEinExpr(sum(tensors; skip=_openinds), sizedict)
+  externalinds_tn = collect(externalinds(tn))
+  expr = SizedEinExpr(sum(tensors; skip=externalinds_tn), sizedict)
 
   return einexpr(optimizer, expr)
 end
@@ -47,15 +48,16 @@ function ITensorNetworks.contraction_sequence(
   tensor_map = Dict{Set{IndexType},VertexType}()
   sizedict = Dict{IndexType,Int}()
 
-  for (key, tensor) in pairs(vertex_data(tn))
-    _inds = collect(inds(tensor))
-    push!(tensors, EinExpr{IndexType}(; head=_inds))
-    tensor_map[Set(_inds)] = key
-    merge!(sizedict, Dict(_inds .=> size(tensor)))
+  for v in vertices(tn)
+    tensor_v = tn[v]
+    inds_v = collect(inds(tensor_v))
+    push!(tensors, EinExpr{IndexType}(; head=inds_v))
+    tensor_map[Set(inds_v)] = key
+    merge!(sizedict, Dict(inds_v .=> size(tensor_v)))
   end
 
-  _openinds = collect(externalinds(tn))
-  expr = SizedEinExpr(sum(tensors; skip=_openinds), sizedict)
+  externalinds_tn = collect(externalinds(tn))
+  expr = SizedEinExpr(sum(tensors; skip=externalinds_tn), sizedict)
 
   path = einexpr(optimizer, expr)
 

From 05f5c3f3107cc487b1f6d15e0ad57ea95b1969e2 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Sergio=20S=C3=A1nchez=20Ram=C3=ADrez?=
 <sergio.sanchez.ramirez+git@bsc.es>
Date: Tue, 6 Feb 2024 16:15:07 +0100
Subject: [PATCH 24/49] Remove duplicated code

---
 .../src/ITensorNetworksEinExprsExt.jl         | 27 +++++--------------
 1 file changed, 7 insertions(+), 20 deletions(-)

diff --git a/ext/ITensorNetworksEinExprsExt/src/ITensorNetworksEinExprsExt.jl b/ext/ITensorNetworksEinExprsExt/src/ITensorNetworksEinExprsExt.jl
index b146b482..85da5b38 100644
--- a/ext/ITensorNetworksEinExprsExt/src/ITensorNetworksEinExprsExt.jl
+++ b/ext/ITensorNetworksEinExprsExt/src/ITensorNetworksEinExprsExt.jl
@@ -10,7 +10,7 @@ using ITensorNetworks:
   contraction_sequence
 using EinExprs: EinExprs, EinExpr, einexpr, SizedEinExpr
 
-function EinExprs.einexpr(tn::ITensorNetwork; optimizer::EinExprs.Optimizer)
+function prepare_einexpr(tn::ITensorNetwork)
   IndexType = Any
   VertexType = vertextype(tn)
 
@@ -29,6 +29,11 @@ function EinExprs.einexpr(tn::ITensorNetwork; optimizer::EinExprs.Optimizer)
   externalinds_tn = collect(externalinds(tn))
   expr = SizedEinExpr(sum(tensors; skip=externalinds_tn), sizedict)
 
+  return expr, tensor_map
+end
+
+function EinExprs.einexpr(tn::ITensorNetwork; optimizer::EinExprs.Optimizer)
+  expr, _ = prepare_einexpr(tn)
   return einexpr(optimizer, expr)
 end
 
@@ -41,25 +46,7 @@ end
 function ITensorNetworks.contraction_sequence(
   ::Algorithm"einexpr", tn::ITensorNetwork{T}; optimizer=EinExprs.Exhaustive()
 )
-  IndexType = Any
-  VertexType = vertextype(tn)
-
-  tensors = EinExpr{IndexType}[]
-  tensor_map = Dict{Set{IndexType},VertexType}()
-  sizedict = Dict{IndexType,Int}()
-
-  for v in vertices(tn)
-    tensor_v = tn[v]
-    inds_v = collect(inds(tensor_v))
-    push!(tensors, EinExpr{IndexType}(; head=inds_v))
-    tensor_map[Set(inds_v)] = key
-    merge!(sizedict, Dict(inds_v .=> size(tensor_v)))
-  end
-
-  externalinds_tn = collect(externalinds(tn))
-  expr = SizedEinExpr(sum(tensors; skip=externalinds_tn), sizedict)
-
-  path = einexpr(optimizer, expr)
+  path, tensor_map = prepare_einexpr(tn)
 
   function _convert_to_contraction_sequence(subpath)
     EinExprs.nargs(subpath) == 0 && return tensor_map[Set(subpath.head)]

From f25bb137978c59008cbdb0ae0cf3e821d2355764 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Sergio=20S=C3=A1nchez=20Ram=C3=ADrez?=
 <sergio.sanchez.ramirez+git@bsc.es>
Date: Tue, 6 Feb 2024 16:17:20 +0100
Subject: [PATCH 25/49] Rename `tensors` to `tensor_exprs`

---
 .../src/ITensorNetworksEinExprsExt.jl                       | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/ext/ITensorNetworksEinExprsExt/src/ITensorNetworksEinExprsExt.jl b/ext/ITensorNetworksEinExprsExt/src/ITensorNetworksEinExprsExt.jl
index 85da5b38..450e34f2 100644
--- a/ext/ITensorNetworksEinExprsExt/src/ITensorNetworksEinExprsExt.jl
+++ b/ext/ITensorNetworksEinExprsExt/src/ITensorNetworksEinExprsExt.jl
@@ -14,20 +14,20 @@ function prepare_einexpr(tn::ITensorNetwork)
   IndexType = Any
   VertexType = vertextype(tn)
 
-  tensors = EinExpr{IndexType}[]
+  tensor_exprs = EinExpr{IndexType}[]
   tensor_map = Dict{Set{IndexType},VertexType}()
   sizedict = Dict{IndexType,Int}()
 
   for v in vertices(tn)
     tensor_v = tn[v]
     inds_v = collect(inds(tensor_v))
-    push!(tensors, EinExpr{IndexType}(; head=inds_v))
+    push!(tensor_exprs, EinExpr{IndexType}(; head=inds_v))
     tensor_map[Set(inds_v)] = key
     merge!(sizedict, Dict(inds_v .=> size(tensor_v)))
   end
 
   externalinds_tn = collect(externalinds(tn))
-  expr = SizedEinExpr(sum(tensors; skip=externalinds_tn), sizedict)
+  expr = SizedEinExpr(sum(tensor_exprs; skip=externalinds_tn), sizedict)
 
   return expr, tensor_map
 end

From 864dd597d2c7b1ee21bfe8c7fdb31bdbc1c29fa6 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Sergio=20S=C3=A1nchez=20Ram=C3=ADrez?=
 <sergio.sanchez.ramirez+git@bsc.es>
Date: Tue, 6 Feb 2024 16:20:11 +0100
Subject: [PATCH 26/49] Define `to_contraction_sequence` in the global scope

---
 .../src/ITensorNetworksEinExprsExt.jl                 | 11 +++++------
 1 file changed, 5 insertions(+), 6 deletions(-)

diff --git a/ext/ITensorNetworksEinExprsExt/src/ITensorNetworksEinExprsExt.jl b/ext/ITensorNetworksEinExprsExt/src/ITensorNetworksEinExprsExt.jl
index 450e34f2..b2a7e5ab 100644
--- a/ext/ITensorNetworksEinExprsExt/src/ITensorNetworksEinExprsExt.jl
+++ b/ext/ITensorNetworksEinExprsExt/src/ITensorNetworksEinExprsExt.jl
@@ -47,13 +47,12 @@ function ITensorNetworks.contraction_sequence(
   ::Algorithm"einexpr", tn::ITensorNetwork{T}; optimizer=EinExprs.Exhaustive()
 )
   path, tensor_map = prepare_einexpr(tn)
+  return to_contraction_sequence(tensor_map, path)
+end
 
-  function _convert_to_contraction_sequence(subpath)
-    EinExprs.nargs(subpath) == 0 && return tensor_map[Set(subpath.head)]
-    return map(_convert_to_contraction_sequence, EinExprs.args(subpath))
-  end
-
-  return _convert_to_contraction_sequence(path)
+function to_contraction_sequence(tensor_map, path)
+  EinExprs.nargs(path) == 0 && return tensor_map[Set(path.head)]
+  return map(_convert_to_contraction_sequence, EinExprs.args(path))
 end
 
 end

From 7c92cc1cacce3b093cbe4bc860e460d6af0152e8 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Sergio=20S=C3=A1nchez=20Ram=C3=ADrez?=
 <sergio.sanchez.ramirez+git@bsc.es>
Date: Tue, 6 Feb 2024 16:21:13 +0100
Subject: [PATCH 27/49] Apply style suggestion by @mtfishman

---
 .../src/ITensorNetworksEinExprsExt.jl                       | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/ext/ITensorNetworksEinExprsExt/src/ITensorNetworksEinExprsExt.jl b/ext/ITensorNetworksEinExprsExt/src/ITensorNetworksEinExprsExt.jl
index b2a7e5ab..924a582b 100644
--- a/ext/ITensorNetworksEinExprsExt/src/ITensorNetworksEinExprsExt.jl
+++ b/ext/ITensorNetworksEinExprsExt/src/ITensorNetworksEinExprsExt.jl
@@ -16,18 +16,18 @@ function prepare_einexpr(tn::ITensorNetwork)
 
   tensor_exprs = EinExpr{IndexType}[]
   tensor_map = Dict{Set{IndexType},VertexType}()
-  sizedict = Dict{IndexType,Int}()
+  inds_dims = Dict{IndexType,Int}()
 
   for v in vertices(tn)
     tensor_v = tn[v]
     inds_v = collect(inds(tensor_v))
     push!(tensor_exprs, EinExpr{IndexType}(; head=inds_v))
     tensor_map[Set(inds_v)] = key
-    merge!(sizedict, Dict(inds_v .=> size(tensor_v)))
+    merge!(inds_dims, Dict(inds_v .=> size(tensor_v)))
   end
 
   externalinds_tn = collect(externalinds(tn))
-  expr = SizedEinExpr(sum(tensor_exprs; skip=externalinds_tn), sizedict)
+  expr = SizedEinExpr(sum(tensor_exprs; skip=externalinds_tn), inds_dims)
 
   return expr, tensor_map
 end

From cad581d97fda5470b007df16b80e6c5a975b0465 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Sergio=20S=C3=A1nchez=20Ram=C3=ADrez?=
 <sergio.sanchez.ramirez+git@bsc.es>
Date: Tue, 6 Feb 2024 16:22:36 +0100
Subject: [PATCH 28/49] Rename `tensor_map` to `tensor_inds_to_vertex`

---
 .../src/ITensorNetworksEinExprsExt.jl              | 14 +++++++-------
 1 file changed, 7 insertions(+), 7 deletions(-)

diff --git a/ext/ITensorNetworksEinExprsExt/src/ITensorNetworksEinExprsExt.jl b/ext/ITensorNetworksEinExprsExt/src/ITensorNetworksEinExprsExt.jl
index 924a582b..f34fc32e 100644
--- a/ext/ITensorNetworksEinExprsExt/src/ITensorNetworksEinExprsExt.jl
+++ b/ext/ITensorNetworksEinExprsExt/src/ITensorNetworksEinExprsExt.jl
@@ -15,21 +15,21 @@ function prepare_einexpr(tn::ITensorNetwork)
   VertexType = vertextype(tn)
 
   tensor_exprs = EinExpr{IndexType}[]
-  tensor_map = Dict{Set{IndexType},VertexType}()
+  tensor_inds_to_vertex = Dict{Set{IndexType},VertexType}()
   inds_dims = Dict{IndexType,Int}()
 
   for v in vertices(tn)
     tensor_v = tn[v]
     inds_v = collect(inds(tensor_v))
     push!(tensor_exprs, EinExpr{IndexType}(; head=inds_v))
-    tensor_map[Set(inds_v)] = key
+    tensor_inds_to_vertex[Set(inds_v)] = key
     merge!(inds_dims, Dict(inds_v .=> size(tensor_v)))
   end
 
   externalinds_tn = collect(externalinds(tn))
   expr = SizedEinExpr(sum(tensor_exprs; skip=externalinds_tn), inds_dims)
 
-  return expr, tensor_map
+  return expr, tensor_inds_to_vertex
 end
 
 function EinExprs.einexpr(tn::ITensorNetwork; optimizer::EinExprs.Optimizer)
@@ -46,12 +46,12 @@ end
 function ITensorNetworks.contraction_sequence(
   ::Algorithm"einexpr", tn::ITensorNetwork{T}; optimizer=EinExprs.Exhaustive()
 )
-  path, tensor_map = prepare_einexpr(tn)
-  return to_contraction_sequence(tensor_map, path)
+  path, tensor_inds_to_vertex = prepare_einexpr(tn)
+  return to_contraction_sequence(tensor_inds_to_vertex, path)
 end
 
-function to_contraction_sequence(tensor_map, path)
-  EinExprs.nargs(path) == 0 && return tensor_map[Set(path.head)]
+function to_contraction_sequence(tensor_inds_to_vertex, path)
+  EinExprs.nargs(path) == 0 && return tensor_inds_to_vertex[Set(path.head)]
   return map(_convert_to_contraction_sequence, EinExprs.args(path))
 end
 

From e9b4aea481e11ead181d5d09fd57641d7f663b76 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Sergio=20S=C3=A1nchez=20Ram=C3=ADrez?=
 <sergio.sanchez.ramirez+git@bsc.es>
Date: Tue, 6 Feb 2024 16:27:11 +0100
Subject: [PATCH 29/49] Apply style suggestion by @mtfishman

---
 .../src/ITensorNetworksEinExprsExt.jl                  | 10 +++++-----
 1 file changed, 5 insertions(+), 5 deletions(-)

diff --git a/ext/ITensorNetworksEinExprsExt/src/ITensorNetworksEinExprsExt.jl b/ext/ITensorNetworksEinExprsExt/src/ITensorNetworksEinExprsExt.jl
index f34fc32e..40b25898 100644
--- a/ext/ITensorNetworksEinExprsExt/src/ITensorNetworksEinExprsExt.jl
+++ b/ext/ITensorNetworksEinExprsExt/src/ITensorNetworksEinExprsExt.jl
@@ -46,13 +46,13 @@ end
 function ITensorNetworks.contraction_sequence(
   ::Algorithm"einexpr", tn::ITensorNetwork{T}; optimizer=EinExprs.Exhaustive()
 )
-  path, tensor_inds_to_vertex = prepare_einexpr(tn)
-  return to_contraction_sequence(tensor_inds_to_vertex, path)
+  expr, tensor_inds_to_vertex = to_einexpr(tn)
+  return to_contraction_sequence(tensor_inds_to_vertex, expr)
 end
 
-function to_contraction_sequence(tensor_inds_to_vertex, path)
-  EinExprs.nargs(path) == 0 && return tensor_inds_to_vertex[Set(path.head)]
-  return map(_convert_to_contraction_sequence, EinExprs.args(path))
+function to_contraction_sequence(tensor_inds_to_vertex, expr)
+  EinExprs.nargs(expr) == 0 && return tensor_inds_to_vertex[Set(expr.head)]
+  return map(_convert_to_contraction_sequence, EinExprs.args(expr))
 end
 
 end

From 43341eee51db4316f15b6549a0a7f6a2d45a3295 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Sergio=20S=C3=A1nchez=20Ram=C3=ADrez?=
 <sergio.sanchez.ramirez+git@bsc.es>
Date: Tue, 6 Feb 2024 16:28:13 +0100
Subject: [PATCH 30/49] Reorder args in `to_contraction_sequence`

---
 .../src/ITensorNetworksEinExprsExt.jl                         | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/ext/ITensorNetworksEinExprsExt/src/ITensorNetworksEinExprsExt.jl b/ext/ITensorNetworksEinExprsExt/src/ITensorNetworksEinExprsExt.jl
index 40b25898..3ebd0fae 100644
--- a/ext/ITensorNetworksEinExprsExt/src/ITensorNetworksEinExprsExt.jl
+++ b/ext/ITensorNetworksEinExprsExt/src/ITensorNetworksEinExprsExt.jl
@@ -47,10 +47,10 @@ function ITensorNetworks.contraction_sequence(
   ::Algorithm"einexpr", tn::ITensorNetwork{T}; optimizer=EinExprs.Exhaustive()
 )
   expr, tensor_inds_to_vertex = to_einexpr(tn)
-  return to_contraction_sequence(tensor_inds_to_vertex, expr)
+  return to_contraction_sequence(expr, tensor_inds_to_vertex)
 end
 
-function to_contraction_sequence(tensor_inds_to_vertex, expr)
+function to_contraction_sequence(expr, tensor_inds_to_vertex)
   EinExprs.nargs(expr) == 0 && return tensor_inds_to_vertex[Set(expr.head)]
   return map(_convert_to_contraction_sequence, EinExprs.args(expr))
 end

From d43f7717cbdc7de212b60b3602e1eb31d458f39b Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Sergio=20S=C3=A1nchez=20Ram=C3=ADrez?=
 <sergio.sanchez.ramirez+git@bsc.es>
Date: Tue, 6 Feb 2024 16:28:50 +0100
Subject: [PATCH 31/49] Rename `prepare_einexpr` to `to_einexpr`

---
 .../src/ITensorNetworksEinExprsExt.jl                         | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/ext/ITensorNetworksEinExprsExt/src/ITensorNetworksEinExprsExt.jl b/ext/ITensorNetworksEinExprsExt/src/ITensorNetworksEinExprsExt.jl
index 3ebd0fae..6a4d92c8 100644
--- a/ext/ITensorNetworksEinExprsExt/src/ITensorNetworksEinExprsExt.jl
+++ b/ext/ITensorNetworksEinExprsExt/src/ITensorNetworksEinExprsExt.jl
@@ -10,7 +10,7 @@ using ITensorNetworks:
   contraction_sequence
 using EinExprs: EinExprs, EinExpr, einexpr, SizedEinExpr
 
-function prepare_einexpr(tn::ITensorNetwork)
+function to_einexpr(tn::ITensorNetwork)
   IndexType = Any
   VertexType = vertextype(tn)
 
@@ -33,7 +33,7 @@ function prepare_einexpr(tn::ITensorNetwork)
 end
 
 function EinExprs.einexpr(tn::ITensorNetwork; optimizer::EinExprs.Optimizer)
-  expr, _ = prepare_einexpr(tn)
+  expr, _ = to_einexpr(tn)
   return einexpr(optimizer, expr)
 end
 

From f399b78bbc6a5a3213121cba2cdb20f8f59bd6f7 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Sergio=20S=C3=A1nchez=20Ram=C3=ADrez?=
 <sergio.sanchez.ramirez+git@bsc.es>
Date: Tue, 6 Feb 2024 16:58:38 +0100
Subject: [PATCH 32/49] Fix call to renamed function

---
 .../src/ITensorNetworksEinExprsExt.jl                           | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/ext/ITensorNetworksEinExprsExt/src/ITensorNetworksEinExprsExt.jl b/ext/ITensorNetworksEinExprsExt/src/ITensorNetworksEinExprsExt.jl
index 6a4d92c8..9af3060a 100644
--- a/ext/ITensorNetworksEinExprsExt/src/ITensorNetworksEinExprsExt.jl
+++ b/ext/ITensorNetworksEinExprsExt/src/ITensorNetworksEinExprsExt.jl
@@ -52,7 +52,7 @@ end
 
 function to_contraction_sequence(expr, tensor_inds_to_vertex)
   EinExprs.nargs(expr) == 0 && return tensor_inds_to_vertex[Set(expr.head)]
-  return map(_convert_to_contraction_sequence, EinExprs.args(expr))
+  return map(to_contraction_sequence, EinExprs.args(expr))
 end
 
 end

From 6c48bbd55a43c5406536a4163c49e0e55eb4272a Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Sergio=20S=C3=A1nchez=20Ram=C3=ADrez?=
 <15837247+mofeing@users.noreply.github.com>
Date: Wed, 7 Feb 2024 02:31:15 +0100
Subject: [PATCH 33/49] Update
 ext/ITensorNetworksEinExprsExt/src/ITensorNetworksEinExprsExt.jl

Co-authored-by: Matt Fishman <mtfishman@users.noreply.github.com>
---
 .../src/ITensorNetworksEinExprsExt.jl                           | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/ext/ITensorNetworksEinExprsExt/src/ITensorNetworksEinExprsExt.jl b/ext/ITensorNetworksEinExprsExt/src/ITensorNetworksEinExprsExt.jl
index 9af3060a..2c37b2b6 100644
--- a/ext/ITensorNetworksEinExprsExt/src/ITensorNetworksEinExprsExt.jl
+++ b/ext/ITensorNetworksEinExprsExt/src/ITensorNetworksEinExprsExt.jl
@@ -52,7 +52,7 @@ end
 
 function to_contraction_sequence(expr, tensor_inds_to_vertex)
   EinExprs.nargs(expr) == 0 && return tensor_inds_to_vertex[Set(expr.head)]
-  return map(to_contraction_sequence, EinExprs.args(expr))
+  return map(expr -> to_contraction_sequence(expr, tensor_inds_to_vertex), EinExprs.args(expr))
 end
 
 end

From cc19993c686b60cb7b14b1799f513d77df3a0ee7 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Sergio=20S=C3=A1nchez=20Ram=C3=ADrez?=
 <sergio.sanchez.ramirez+git@bsc.es>
Date: Wed, 7 Feb 2024 16:33:46 +0100
Subject: [PATCH 34/49] Move out vertex mapping from `to_einexpr` to
 `tensor_inds_to_vertex`

---
 .../src/ITensorNetworksEinExprsExt.jl         | 25 ++++++++++++-------
 1 file changed, 16 insertions(+), 9 deletions(-)

diff --git a/ext/ITensorNetworksEinExprsExt/src/ITensorNetworksEinExprsExt.jl b/ext/ITensorNetworksEinExprsExt/src/ITensorNetworksEinExprsExt.jl
index 2c37b2b6..5767be8e 100644
--- a/ext/ITensorNetworksEinExprsExt/src/ITensorNetworksEinExprsExt.jl
+++ b/ext/ITensorNetworksEinExprsExt/src/ITensorNetworksEinExprsExt.jl
@@ -10,30 +10,37 @@ using ITensorNetworks:
   contraction_sequence
 using EinExprs: EinExprs, EinExpr, einexpr, SizedEinExpr
 
-function to_einexpr(tn::ITensorNetwork)
+function to_einexpr(tn::AbstractITensorNetwork)
   IndexType = Any
-  VertexType = vertextype(tn)
 
   tensor_exprs = EinExpr{IndexType}[]
-  tensor_inds_to_vertex = Dict{Set{IndexType},VertexType}()
   inds_dims = Dict{IndexType,Int}()
 
   for v in vertices(tn)
     tensor_v = tn[v]
     inds_v = collect(inds(tensor_v))
     push!(tensor_exprs, EinExpr{IndexType}(; head=inds_v))
-    tensor_inds_to_vertex[Set(inds_v)] = key
     merge!(inds_dims, Dict(inds_v .=> size(tensor_v)))
   end
 
   externalinds_tn = collect(externalinds(tn))
-  expr = SizedEinExpr(sum(tensor_exprs; skip=externalinds_tn), inds_dims)
+  return SizedEinExpr(sum(tensor_exprs; skip=externalinds_tn), inds_dims)
+end
+
+function tensor_inds_to_vertex(tn::AbstractITensorNetwork)
+  mapping = Dict{Set{IndexType},VertexType}()
+
+  for v in vertices(tn)
+    tensor_v = tn[v]
+    inds_v = collect(inds(tensor_v))
+    mapping[Set(inds_v)] = v
+  end
 
-  return expr, tensor_inds_to_vertex
+  return mapping
 end
 
 function EinExprs.einexpr(tn::ITensorNetwork; optimizer::EinExprs.Optimizer)
-  expr, _ = to_einexpr(tn)
+  expr = to_einexpr(tn)
   return einexpr(optimizer, expr)
 end
 
@@ -46,8 +53,8 @@ end
 function ITensorNetworks.contraction_sequence(
   ::Algorithm"einexpr", tn::ITensorNetwork{T}; optimizer=EinExprs.Exhaustive()
 )
-  expr, tensor_inds_to_vertex = to_einexpr(tn)
-  return to_contraction_sequence(expr, tensor_inds_to_vertex)
+  expr = einexpr(tn; optimizer)
+  return to_contraction_sequence(expr, tensor_inds_to_vertex(tn))
 end
 
 function to_contraction_sequence(expr, tensor_inds_to_vertex)

From c2d9f9d59d1784308219ac691fac1e3196ffe713 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Sergio=20S=C3=A1nchez=20Ram=C3=ADrez?=
 <sergio.sanchez.ramirez+git@bsc.es>
Date: Wed, 7 Feb 2024 21:49:25 +0100
Subject: [PATCH 35/49] Apply suggestions by @JoeyT1994

---
 .../src/ITensorNetworksEinExprsExt.jl         | 21 +++++++------------
 1 file changed, 7 insertions(+), 14 deletions(-)

diff --git a/ext/ITensorNetworksEinExprsExt/src/ITensorNetworksEinExprsExt.jl b/ext/ITensorNetworksEinExprsExt/src/ITensorNetworksEinExprsExt.jl
index 5767be8e..81984f45 100644
--- a/ext/ITensorNetworksEinExprsExt/src/ITensorNetworksEinExprsExt.jl
+++ b/ext/ITensorNetworksEinExprsExt/src/ITensorNetworksEinExprsExt.jl
@@ -1,37 +1,30 @@
 module ITensorNetworksEinExprsExt
 
-using ITensors: Index, ITensor, Algorithm
+using ITensors: Index, ITensor, Algorithm, noncommoninds
 using ITensorNetworks:
-  ITensorNetworks,
-  ITensorNetwork,
-  vertextype,
-  vertex_data,
-  externalinds,
-  contraction_sequence
+  ITensorNetworks, ITensorNetwork, vertextype, vertex_data, contraction_sequence
 using EinExprs: EinExprs, EinExpr, einexpr, SizedEinExpr
 
-function to_einexpr(tn::AbstractITensorNetwork)
+function to_einexpr(ts::Vector{ITensor})
   IndexType = Any
 
   tensor_exprs = EinExpr{IndexType}[]
   inds_dims = Dict{IndexType,Int}()
 
-  for v in vertices(tn)
-    tensor_v = tn[v]
+  for tensor_v in ts
     inds_v = collect(inds(tensor_v))
     push!(tensor_exprs, EinExpr{IndexType}(; head=inds_v))
     merge!(inds_dims, Dict(inds_v .=> size(tensor_v)))
   end
 
-  externalinds_tn = collect(externalinds(tn))
+  externalinds_tn = collect(noncommoninds(ts...))
   return SizedEinExpr(sum(tensor_exprs; skip=externalinds_tn), inds_dims)
 end
 
-function tensor_inds_to_vertex(tn::AbstractITensorNetwork)
+function tensor_inds_to_vertex(ts::Vector{ITensor})
   mapping = Dict{Set{IndexType},VertexType}()
 
-  for v in vertices(tn)
-    tensor_v = tn[v]
+  for (v, tensor_v) in enumerate(ts)
     inds_v = collect(inds(tensor_v))
     mapping[Set(inds_v)] = v
   end

From 1d43c4b978a7d3e7f5c79542c77bba448625cefc Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Sergio=20S=C3=A1nchez=20Ram=C3=ADrez?=
 <sergio.sanchez.ramirez+git@bsc.es>
Date: Wed, 7 Feb 2024 21:54:57 +0100
Subject: [PATCH 36/49] Apply suggestion by @JoeyT1994

---
 .../src/ITensorNetworksEinExprsExt.jl         | 22 ++++++-------------
 1 file changed, 7 insertions(+), 15 deletions(-)

diff --git a/ext/ITensorNetworksEinExprsExt/src/ITensorNetworksEinExprsExt.jl b/ext/ITensorNetworksEinExprsExt/src/ITensorNetworksEinExprsExt.jl
index 81984f45..ab8f9e4c 100644
--- a/ext/ITensorNetworksEinExprsExt/src/ITensorNetworksEinExprsExt.jl
+++ b/ext/ITensorNetworksEinExprsExt/src/ITensorNetworksEinExprsExt.jl
@@ -32,27 +32,19 @@ function tensor_inds_to_vertex(ts::Vector{ITensor})
   return mapping
 end
 
-function EinExprs.einexpr(tn::ITensorNetwork; optimizer::EinExprs.Optimizer)
-  expr = to_einexpr(tn)
-  return einexpr(optimizer, expr)
-end
-
-function ITensorNetworks.contraction_sequence(
-  alg::Algorithm"einexpr", tn::Vector{ITensor}; kwargs...
-)
-  return contraction_sequence(alg, ITensorNetwork(tn); kwargs...)
-end
-
 function ITensorNetworks.contraction_sequence(
-  ::Algorithm"einexpr", tn::ITensorNetwork{T}; optimizer=EinExprs.Exhaustive()
+  ::Algorithm"einexpr", tn::Vector{ITensor}; optimizer=EinExprs.Exhaustive()
 )
-  expr = einexpr(tn; optimizer)
-  return to_contraction_sequence(expr, tensor_inds_to_vertex(tn))
+  expr = to_einexpr(tn)
+  path = einexpr(expr; kwargs...)
+  return to_contraction_sequence(path, tensor_inds_to_vertex(tn))
 end
 
 function to_contraction_sequence(expr, tensor_inds_to_vertex)
   EinExprs.nargs(expr) == 0 && return tensor_inds_to_vertex[Set(expr.head)]
-  return map(expr -> to_contraction_sequence(expr, tensor_inds_to_vertex), EinExprs.args(expr))
+  return map(
+    expr -> to_contraction_sequence(expr, tensor_inds_to_vertex), EinExprs.args(expr)
+  )
 end
 
 end

From 8ed06795238b06d1093741c260aa2cc5964bfeb6 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Sergio=20S=C3=A1nchez=20Ram=C3=ADrez?=
 <15837247+mofeing@users.noreply.github.com>
Date: Thu, 8 Feb 2024 00:30:11 +0100
Subject: [PATCH 37/49] Update
 ext/ITensorNetworksEinExprsExt/src/ITensorNetworksEinExprsExt.jl

Co-authored-by: Matt Fishman <mtfishman@users.noreply.github.com>
---
 .../src/ITensorNetworksEinExprsExt.jl                           | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/ext/ITensorNetworksEinExprsExt/src/ITensorNetworksEinExprsExt.jl b/ext/ITensorNetworksEinExprsExt/src/ITensorNetworksEinExprsExt.jl
index ab8f9e4c..cf3d0866 100644
--- a/ext/ITensorNetworksEinExprsExt/src/ITensorNetworksEinExprsExt.jl
+++ b/ext/ITensorNetworksEinExprsExt/src/ITensorNetworksEinExprsExt.jl
@@ -17,7 +17,7 @@ function to_einexpr(ts::Vector{ITensor})
     merge!(inds_dims, Dict(inds_v .=> size(tensor_v)))
   end
 
-  externalinds_tn = collect(noncommoninds(ts...))
+  externalinds_tn = reduce(noncommoninds, ts)
   return SizedEinExpr(sum(tensor_exprs; skip=externalinds_tn), inds_dims)
 end
 

From f07754d3d741df67fc4bdad4c856eb278453353a Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Sergio=20S=C3=A1nchez=20Ram=C3=ADrez?=
 <sergio.sanchez.ramirez+git@bsc.es>
Date: Thu, 8 Feb 2024 00:32:22 +0100
Subject: [PATCH 38/49] Refactor test as suggested by @mtfishman

---
 test/test_contraction_sequence.jl | 13 ++++++-------
 1 file changed, 6 insertions(+), 7 deletions(-)

diff --git a/test/test_contraction_sequence.jl b/test/test_contraction_sequence.jl
index 2184db22..1271bfb5 100644
--- a/test/test_contraction_sequence.jl
+++ b/test/test_contraction_sequence.jl
@@ -30,13 +30,12 @@ ITensors.disable_warn_order()
   res_einexprs_greedy = contract(tn; sequence=seq_einexprs_exhaustive)[]
   seq_einexprs_kahypar = contraction_sequence(tn; alg="einexpr", optimizer=HyPar())
   res_einexprs_kahypar = contract(tn; sequence=seq_einexprs_kahypar)[]
-  @test res_optimal ≈
-    res_greedy ≈
-    res_tree_sa ≈
-    res_sa_bipartite ≈
-    res_einexprs_exhaustive ≈
-    res_einexprs_greedy ≈
-    res_einexprs_kahypar
+  @test res_greedy ≈ res_optimal
+  @test res_tree_sa ≈ res_optimal
+  @test res_sa_bipartite ≈ res_optimal
+  @test res_einexprs_exhaustive ≈ res_optimal
+  @test res_einexprs_greedy ≈ res_optimal
+  @test res_einexprs_kahypar ≈ res_optimal
 
   if !Sys.iswindows()
     # KaHyPar doesn't work on Windows

From 8c8328dc410d1620ddcfb3471955b8ba8f62a255 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Sergio=20S=C3=A1nchez=20Ram=C3=ADrez?=
 <sergio.sanchez.ramirez+git@bsc.es>
Date: Thu, 8 Feb 2024 21:54:53 +0100
Subject: [PATCH 39/49] Duplicate weakdeps in extras to support Julia <1.9

---
 Project.toml | 1 +
 1 file changed, 1 insertion(+)

diff --git a/Project.toml b/Project.toml
index 0ee65a49..e53a4b80 100644
--- a/Project.toml
+++ b/Project.toml
@@ -67,6 +67,7 @@ julia = "1.7"
 
 [extras]
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
+EinExprs = "b1794770-133b-4de1-afb4-526377e9f4c5"
 
 [targets]
 test = ["Test"]

From acd7a03384b73ff880057db4808924ffa68412ce Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Sergio=20S=C3=A1nchez=20Ram=C3=ADrez?=
 <sergio.sanchez.ramirez+git@bsc.es>
Date: Mon, 12 Feb 2024 15:26:59 +0000
Subject: [PATCH 40/49] Try fix for package extension path

---
 .../{src => }/ITensorNetworksEinExprsExt.jl                       | 0
 1 file changed, 0 insertions(+), 0 deletions(-)
 rename ext/ITensorNetworksEinExprsExt/{src => }/ITensorNetworksEinExprsExt.jl (100%)

diff --git a/ext/ITensorNetworksEinExprsExt/src/ITensorNetworksEinExprsExt.jl b/ext/ITensorNetworksEinExprsExt/ITensorNetworksEinExprsExt.jl
similarity index 100%
rename from ext/ITensorNetworksEinExprsExt/src/ITensorNetworksEinExprsExt.jl
rename to ext/ITensorNetworksEinExprsExt/ITensorNetworksEinExprsExt.jl

From 7e533f2ff30bee5f78aca107374eedd0abc607fa Mon Sep 17 00:00:00 2001
From: Matt Fishman <mtfishman@users.noreply.github.com>
Date: Mon, 12 Feb 2024 11:29:31 -0500
Subject: [PATCH 41/49] Bring `@Algorithm_str` into the extension namespace

---
 ext/ITensorNetworksEinExprsExt/ITensorNetworksEinExprsExt.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/ext/ITensorNetworksEinExprsExt/ITensorNetworksEinExprsExt.jl b/ext/ITensorNetworksEinExprsExt/ITensorNetworksEinExprsExt.jl
index cf3d0866..01b933b9 100644
--- a/ext/ITensorNetworksEinExprsExt/ITensorNetworksEinExprsExt.jl
+++ b/ext/ITensorNetworksEinExprsExt/ITensorNetworksEinExprsExt.jl
@@ -1,6 +1,6 @@
 module ITensorNetworksEinExprsExt
 
-using ITensors: Index, ITensor, Algorithm, noncommoninds
+using ITensors: Index, ITensor, Algorithm, @Algorithm_str, noncommoninds
 using ITensorNetworks:
   ITensorNetworks, ITensorNetwork, vertextype, vertex_data, contraction_sequence
 using EinExprs: EinExprs, EinExpr, einexpr, SizedEinExpr

From 739e75296060dca6a8d10adb5739634763d46426 Mon Sep 17 00:00:00 2001
From: Matt Fishman <mtfishman@users.noreply.github.com>
Date: Mon, 12 Feb 2024 11:39:53 -0500
Subject: [PATCH 42/49] Remove `Algorithm` from extension namespace

---
 ext/ITensorNetworksEinExprsExt/ITensorNetworksEinExprsExt.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/ext/ITensorNetworksEinExprsExt/ITensorNetworksEinExprsExt.jl b/ext/ITensorNetworksEinExprsExt/ITensorNetworksEinExprsExt.jl
index 01b933b9..06d34763 100644
--- a/ext/ITensorNetworksEinExprsExt/ITensorNetworksEinExprsExt.jl
+++ b/ext/ITensorNetworksEinExprsExt/ITensorNetworksEinExprsExt.jl
@@ -1,6 +1,6 @@
 module ITensorNetworksEinExprsExt
 
-using ITensors: Index, ITensor, Algorithm, @Algorithm_str, noncommoninds
+using ITensors: Index, ITensor, @Algorithm_str, noncommoninds
 using ITensorNetworks:
   ITensorNetworks, ITensorNetwork, vertextype, vertex_data, contraction_sequence
 using EinExprs: EinExprs, EinExpr, einexpr, SizedEinExpr

From 6acf91ab7a0ff42826f8cf5976587b4017bea043 Mon Sep 17 00:00:00 2001
From: Matt Fishman <mtfishman@users.noreply.github.com>
Date: Mon, 12 Feb 2024 13:03:21 -0500
Subject: [PATCH 43/49] Bring `inds` into the extension namespace

---
 ext/ITensorNetworksEinExprsExt/ITensorNetworksEinExprsExt.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/ext/ITensorNetworksEinExprsExt/ITensorNetworksEinExprsExt.jl b/ext/ITensorNetworksEinExprsExt/ITensorNetworksEinExprsExt.jl
index 06d34763..cdca6c3d 100644
--- a/ext/ITensorNetworksEinExprsExt/ITensorNetworksEinExprsExt.jl
+++ b/ext/ITensorNetworksEinExprsExt/ITensorNetworksEinExprsExt.jl
@@ -1,6 +1,6 @@
 module ITensorNetworksEinExprsExt
 
-using ITensors: Index, ITensor, @Algorithm_str, noncommoninds
+using ITensors: Index, ITensor, @Algorithm_str, inds, noncommoninds
 using ITensorNetworks:
   ITensorNetworks, ITensorNetwork, vertextype, vertex_data, contraction_sequence
 using EinExprs: EinExprs, EinExpr, einexpr, SizedEinExpr

From bd132eb6bf2ae68e1a28378b7aa274f5a5c2a314 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Sergio=20S=C3=A1nchez=20Ram=C3=ADrez?=
 <sergio.sanchez.ramirez+git@bsc.es>
Date: Tue, 13 Feb 2024 13:10:53 +0000
Subject: [PATCH 44/49] Fix typo

---
 ext/ITensorNetworksEinExprsExt/ITensorNetworksEinExprsExt.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/ext/ITensorNetworksEinExprsExt/ITensorNetworksEinExprsExt.jl b/ext/ITensorNetworksEinExprsExt/ITensorNetworksEinExprsExt.jl
index cdca6c3d..ebddb989 100644
--- a/ext/ITensorNetworksEinExprsExt/ITensorNetworksEinExprsExt.jl
+++ b/ext/ITensorNetworksEinExprsExt/ITensorNetworksEinExprsExt.jl
@@ -36,7 +36,7 @@ function ITensorNetworks.contraction_sequence(
   ::Algorithm"einexpr", tn::Vector{ITensor}; optimizer=EinExprs.Exhaustive()
 )
   expr = to_einexpr(tn)
-  path = einexpr(expr; kwargs...)
+  path = einexpr(optimizer, expr)
   return to_contraction_sequence(path, tensor_inds_to_vertex(tn))
 end
 

From d965b14e5610d8ea1616ea48db574a02aa273f13 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Sergio=20S=C3=A1nchez=20Ram=C3=ADrez?=
 <sergio.sanchez.ramirez+git@bsc.es>
Date: Tue, 13 Feb 2024 15:32:25 +0000
Subject: [PATCH 45/49] Fix KaHyPar tests with EinExprs

---
 test/test_contraction_sequence.jl | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/test/test_contraction_sequence.jl b/test/test_contraction_sequence.jl
index 1271bfb5..5470dabe 100644
--- a/test/test_contraction_sequence.jl
+++ b/test/test_contraction_sequence.jl
@@ -28,14 +28,11 @@ ITensors.disable_warn_order()
   res_einexprs_exhaustive = contract(tn; sequence=seq_einexprs_exhaustive)[]
   seq_einexprs_greedy = contraction_sequence(tn; alg="einexpr", optimizer=Greedy())
   res_einexprs_greedy = contract(tn; sequence=seq_einexprs_exhaustive)[]
-  seq_einexprs_kahypar = contraction_sequence(tn; alg="einexpr", optimizer=HyPar())
-  res_einexprs_kahypar = contract(tn; sequence=seq_einexprs_kahypar)[]
   @test res_greedy ≈ res_optimal
   @test res_tree_sa ≈ res_optimal
   @test res_sa_bipartite ≈ res_optimal
   @test res_einexprs_exhaustive ≈ res_optimal
   @test res_einexprs_greedy ≈ res_optimal
-  @test res_einexprs_kahypar ≈ res_optimal
 
   if !Sys.iswindows()
     # KaHyPar doesn't work on Windows
@@ -46,5 +43,8 @@ ITensors.disable_warn_order()
     seq_kahypar_bipartite = contraction_sequence(tn; alg="kahypar_bipartite", sc_target=200)
     res_kahypar_bipartite = contract(tn; sequence=seq_kahypar_bipartite)[]
     @test res_optimal ≈ res_kahypar_bipartite
+    seq_einexprs_kahypar = contraction_sequence(tn; alg="einexpr", optimizer=HyPar())
+    res_einexprs_kahypar = contract(tn; sequence=seq_einexprs_kahypar)[]
+    @test res_einexprs_kahypar ≈ res_optimal
   end
 end

From 47fddf616f93581b8a3315f96ca380979e03ede0 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Sergio=20S=C3=A1nchez=20Ram=C3=ADrez?=
 <15837247+mofeing@users.noreply.github.com>
Date: Tue, 13 Feb 2024 15:40:03 +0000
Subject: [PATCH 46/49] Fix EinExprs version

Co-authored-by: Matt Fishman <mtfishman@users.noreply.github.com>
---
 Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Project.toml b/Project.toml
index e53a4b80..04096e54 100644
--- a/Project.toml
+++ b/Project.toml
@@ -46,7 +46,7 @@ DataStructures = "0.18"
 Dictionaries = "0.3.15"
 Distributions = "0.25.86"
 DocStringExtensions = "0.8, 0.9"
-EinExprs = "0.6"
+EinExprs = "0.6.4"
 Graphs = "1.8"
 GraphsFlows = "0.1.1"
 ITensors = "0.3.23"

From b73ae82abf8d53c1c13cd70c291908c3995fb1bd Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Sergio=20S=C3=A1nchez=20Ram=C3=ADrez?=
 <sergio.sanchez.ramirez+git@bsc.es>
Date: Tue, 13 Feb 2024 15:42:55 +0000
Subject: [PATCH 47/49] Fix missing type definition

---
 ext/ITensorNetworksEinExprsExt/ITensorNetworksEinExprsExt.jl | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/ext/ITensorNetworksEinExprsExt/ITensorNetworksEinExprsExt.jl b/ext/ITensorNetworksEinExprsExt/ITensorNetworksEinExprsExt.jl
index ebddb989..516469da 100644
--- a/ext/ITensorNetworksEinExprsExt/ITensorNetworksEinExprsExt.jl
+++ b/ext/ITensorNetworksEinExprsExt/ITensorNetworksEinExprsExt.jl
@@ -22,6 +22,8 @@ function to_einexpr(ts::Vector{ITensor})
 end
 
 function tensor_inds_to_vertex(ts::Vector{ITensor})
+  IndexType = Any
+
   mapping = Dict{Set{IndexType},VertexType}()
 
   for (v, tensor_v) in enumerate(ts)

From 4c22571a5fa551eca185439c54f6211efa76c23c Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Sergio=20S=C3=A1nchez=20Ram=C3=ADrez?=
 <sergio.sanchez.ramirez+git@bsc.es>
Date: Tue, 13 Feb 2024 17:04:31 +0000
Subject: [PATCH 48/49] Fix missing type definition

---
 ext/ITensorNetworksEinExprsExt/ITensorNetworksEinExprsExt.jl | 1 +
 1 file changed, 1 insertion(+)

diff --git a/ext/ITensorNetworksEinExprsExt/ITensorNetworksEinExprsExt.jl b/ext/ITensorNetworksEinExprsExt/ITensorNetworksEinExprsExt.jl
index 516469da..73d7a847 100644
--- a/ext/ITensorNetworksEinExprsExt/ITensorNetworksEinExprsExt.jl
+++ b/ext/ITensorNetworksEinExprsExt/ITensorNetworksEinExprsExt.jl
@@ -23,6 +23,7 @@ end
 
 function tensor_inds_to_vertex(ts::Vector{ITensor})
   IndexType = Any
+  VertexType = Int
 
   mapping = Dict{Set{IndexType},VertexType}()
 

From 3ec86f2c3cf6b2a6892561b86eff3155397b41b0 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Sergio=20S=C3=A1nchez=20Ram=C3=ADrez?=
 <sergio.sanchez.ramirez+git@bsc.es>
Date: Tue, 13 Feb 2024 18:34:37 +0000
Subject: [PATCH 49/49] Fix package extensions on Julia <1.9

---
 Project.toml           | 3 ++-
 src/ITensorNetworks.jl | 2 ++
 2 files changed, 4 insertions(+), 1 deletion(-)

diff --git a/Project.toml b/Project.toml
index 04096e54..e4375c24 100644
--- a/Project.toml
+++ b/Project.toml
@@ -21,6 +21,7 @@ KrylovKit = "0b1a1467-8014-51b9-945f-bf0ae24f4b77"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 NamedGraphs = "678767b0-92e7-4007-89e4-4527a8725b19"
 Observers = "338f10d5-c7f1-4033-a7d1-f9dec39bcaa0"
+PackageExtensionCompat = "65ce6f38-6b18-4e1d-a461-8949797d7930"
 Printf = "de0858da-6303-5e67-8744-51eddeeeb8d7"
 Requires = "ae029012-a4dd-5104-9daa-d747884805df"
 SimpleTraits = "699a6c99-e7fa-54fc-8d76-47d257e15c1d"
@@ -66,8 +67,8 @@ TupleTools = "1.4"
 julia = "1.7"
 
 [extras]
-Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 EinExprs = "b1794770-133b-4de1-afb4-526377e9f4c5"
+Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
 [targets]
 test = ["Test"]
diff --git a/src/ITensorNetworks.jl b/src/ITensorNetworks.jl
index 24fea311..18b4c88e 100644
--- a/src/ITensorNetworks.jl
+++ b/src/ITensorNetworks.jl
@@ -22,6 +22,7 @@ using LinearAlgebra
 using NamedGraphs
 using Observers
 using Observers.DataFrames: select!
+using PackageExtensionCompat
 using Printf
 using Requires
 using SimpleTraits
@@ -130,6 +131,7 @@ include(joinpath("treetensornetworks", "solvers", "tree_sweeping.jl"))
 include("exports.jl")
 
 function __init__()
+  @require_extensions
   @require OMEinsumContractionOrders = "6f22d1fd-8eed-4bb7-9776-e7d684900715" include(
     joinpath("requires", "omeinsumcontractionorders.jl")
   )